\documentclass[ucs,9pt]{beamer}

% Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
%
% In principle, this file can be redistributed and/or modified under
% the terms of the GNU Public License, version 2.
%
% However, this file is supposed to be a template to be modified
% for your own needs. For this reason, if you use this file as a
% template and not specifically distribute it as part of a another
% package/program, I grant the extra permission to freely copy and
% modify this file as you see fit and even to delete this copyright
% notice.
%
% Modified by Tobias G. Pfeiffer <tobias.pfeiffer@math.fu-berlin.de>
% to show usage of some features specific to the FU Berlin template.

% remove this line and the "ucs" option to the documentclass when your editor is not utf8-capable
\usepackage[utf8x]{inputenc}    % to make utf-8 input possible
\usepackage[english]{babel}     % hyphenation etc., alternatively use 'german' as parameter

\usepackage{hyperref}

\include{fu-beamer-template}  % THIS is the line that includes the FU template!

\usepackage{arev,t1enc} % looks nicer than the standard sans-serif font
% if you experience problems, comment out the line above and change
% the documentclass option "9pt" to "10pt"

% image to be shown on the title page (without file extension, should be pdf or png)
\titleimage{lmt_big.png}

\title{Optimale Triangulation einer beliebigen Punktmenge}

\author[] % (optional, use only with lots of authors)
{Mark Essien, Adam Furmańczuk, Nils Grabenhorst, Andreas Henne, Yuri Lewash, Paul Seiferth}
% - Give the names in the same order as the appear in the paper.

%\institute[FU Berlin] % (optional, but mostly needed)
%{Freie Universität Berlin}
% - Keep it simple, no one is interested in your street address.

\date[2011] % (optional, should be abbreviation of conference name)
{2011}
% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online

\subject{LMT Triangulation}
% This is only inserted into the PDF information catalog. Can be left
% out.

% you can redefine the text shown in the footline. use a combination of
% \insertshortauthor, \insertshortinstitute, \insertshorttitle, \insertshortdate, ...
\renewcommand{\footlinetext}{\insertshortinstitute, \insertshorttitle, \insertshortdate}

\begin{document}

\begin{frame}[plain]
  \titlepage
\end{frame}

\begin{frame}{Outline}
  \tableofcontents
  % You might wish to add the option [pausesections]
\end{frame}

\section{Problemstellung} 
\begin{frame}
\frametitle{Problemstellung} 
\begin{itemize}
 \item Gegeben: Punktmenge $P \subseteq \mathbb{R}$, Gewichtsfunktion $w: T(P) \mapsto \mathbb{R}$ 
 \item Gesucht: $T(P)$ mit $w(T(P))$ ist minimal.
 \item Beispiel: \newline
 \includegraphics<1>[scale=0.5]{punktmenge}
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Problemstellung} 
\begin{itemize}
 \item Gegeben: Punktmenge $P \subseteq \mathbb{R}$, Gewichtsfunktion $w: T(P) \mapsto \mathbb{R}$ 
 \item Gesucht: $T(P)$ mit $w(T(P))$ ist minimal.
 \item Beispiel: \newline
 \includegraphics<1>[scale=0.5]{triangulierung}
\end{itemize}
\end{frame}


\begin{frame}
\frametitle{L\"osungsansatz} 
\begin{itemize}
 \item LMT-Heuristik gibt Teilgraphen der minimalen Triangulierung
 \item \"Ubriggebliebene einfache Polygone mit bekannten Algorithmen triangulieren
 \item Ziele:
  \begin{itemize}
  \item Optimierte Implementierung des LMT Algorithmus
  \item Implementierung verschiedener Gewichtsfunktion und einfaches hinzuf\"ugen von Gewichtsfunktionen
  \item interaktive GUI
  \end{itemize}
\end{itemize}
\end{frame}


\section{Simple LMT Skeleton Implementation} 
\begin{frame}\frametitle{Simple LMT Skeleton Implementation}
\includegraphics<1>[scale=0.2]{lmt_big}
\begin{itemize}
\item erster, voll funktionsfähiger Ansatz
\item einfach und ohne Optimierungen
\end{itemize} 
\end{frame}

\input{optimization.tex}

\input{polygonTriangulation.tex}


% All of the following is optional and typically not needed. 
\appendix
\section<presentation>*{\appendixname}
\subsection<presentation>*{For Further Reading}

\begin{frame}[allowframebreaks]
  \frametitle<presentation>{Quellen}
    
  \begin{thebibliography}{10}
   
  \beamertemplatearticlebibitems
  \end{thebibliography}
\end{frame}

\end{document}
